The validity of using Raoult’s Law, versus using other equations of state, to predict speciated emissions from petroleum storage tanks, was investigated by Radian Corporation for API in 1990[13]. This study used data for two gasolines, summer blend and winter blend. Vapor compositions were predicted from liquid composition data using Raoult’s Law, the RKS equation of state[19], and the PR equation of state[20]. These data were then compared to the measured vapor composition data. Summaries of these results are presented in Tables A.1 and A.2 for summer blend and winter blend gasolines. The measured liquid and vapor concentrations were taken from Wright, Menon, and Peoples[16]; the predicted vapor concentrations were calculated using the ASPEN/SP[21] simulator’s Two-Phase Flash model. Calculations were based on a system temperature of 60 °F.
Table A.1—Summary of Results for Summer Blend Unleaded Gasoline
Toxic Species
Measured a Concentration
(weight percent) Predicted Vapor Concentration (weight percent)
Liquid Vapor Raoult b PR c RKS d
Cyclohexane 0.58 0.20 0.25 0.27 0.26
Benzene 1.93 0.73 0.83 1.05 0.99
Toluene 10.32 0.81 1.29 1.57 1.45
o-Xylene 3.39 0.05 0.00 0.00 0.00
Isomers of xylene 9.16 0.21 0.31 0.33 0.30
Ethylbenzene 2.05 0.05 0.00 0.00 0.00
isopropylbenzene 0.19 — 0.00 0.00 0.00
1,2,4-Trimethylbenzene 3.52 0.04 0.00 0.00 0.00
a Source: References [13] and [16].
b Raoult = Raoult’s Law
c PR = Peng-Robinson equation of state
d RKS = Redlich-Kwong-Soave equation of state
Table A.2—Summary of Results for Winter Blend Unleaded Gasoline
Toxic Species
Measured aConcentration
(weight percent) Predicted Vapor Concentration (weight percent)
Liquid Vapor Raoult b PR c RKS d
Cyclohexane 0.50 0.34 0.16 0.17 0.16
Benzene 1.82 1.43 0.56 0.71 0.67
Toluene 9.11 2.10 0.82 1.00 0.92
o-Xylene 3.59 0.51 0.00 0.00 0.00
Isomers of xylene 8.75 1.02 0.21 0.23 0.00
Ethylbenzene 2.08 0.31 0.00 0.00 0.00
isopropylbenzene 0.19 — 0.00 0.00 0.00
1,2,4-Trimethylbenzene 4.21 0.05 0.00 0.00 0.00
Naphthalene 0.25 — 0.00 0.00 0.00
a Source: References [13] and [16].
b Raoult = Raoult’s Law
c PR = Peng-Robinson equation of state.
d RKS = Redlich-Kwong-Soave equation of state.
Copyright American Petroleum Institute Provided by IHS under license with API
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As presented in Table A.1 for summer blend gasoline, there were no significant differences between the vapor compositions predicted by Raoult’s Law and the two equations of state. All three of the methods predicted vapor concentrations that were higher than the measured vapor concentrations. Results presented in Table A.2 for the winter blend gasoline show there is little difference between Raoult’s Law and the equations of state predictions for vapor compositions. However, all three methods predicted vapor concentrations that were lower than the measured values.
From this study, Radian Corporation concluded that the use of Raoult’s Law in the prediction of vapor compositions from liquid composition data provides essentially the same level of accuracy as those based on the two equations of state, at least for the gasolines included in the assessment. Because gasoline was the only stock investigated in this study, these results could not be generalized to include other stocks of interest, such as crude oils.
In order to further test the validity of the vapor and liquid equilibrium models investigated in 1990[13], the study was continued for API by Radian Corporation in 1991 and the results were reported in 1992[14]. The liquid and vapor equilibrium compositions for selected species in three crude oil samples – mid-continent crude oil, Alaska North Slope (ANS) crude oil, and ANS crude oil spiked with natural gas liquids – were analyzed. Two refined product samples, JP–4 Aviation Fuel and No. 2 Fuel Oil were also analyzed. Twelve compounds were selected to be speciated and are listed in Table A.3.
Table A.3—Compounds Selected for Speciation Butane
n-Hexane Benzene Cyclohexane
Toluene Octane Ethylbenzene
m, p-Xylenes o-Xylene isopropylbenzene 1,2,4-Trimethylbenzene
Naphthalene
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Table A.4—GC Analysis Concentrations Using Average Response Factors (ARF) and Linear Regression (LR) for Liquid Phase Samples (Concentrations in àg/mL)
Compounds
JP-4 Aviation
Fuel
No. 2 Fuel Oil (Mean Value)
Mid-Cont Crude (Mean
Value) Alaska Crude
Spiked Alaska Crude
ARF LR ARF LR ARF LR ARF LR ARF LR
Butane 4280 4280 <250 <300 5900 5730 2120 2120 5680 5680 n-Hexane 19900 18400 <250 <300 9060 7430 7710 6190 8220 6650 Benzene 3880 5010 <250 <300 2560 1370 2770 1560 2640 1440 Cyclohexane 6030 6200 <250 <300 7700 5890 7350 5570 6930 5190 Toluene 29500 28100 300 1040 12200 9960 10800 8690 9060 7100 Octane 8330 8510 483 948 10500 8480 9060 7220 7540 5840 Ethylbenzene 1590 2740 157 793 6420 4880 1780 490 1450 176
m, p-Xylenes 2530 3600 1060 1620 9020 7340 7170 5560 5620 4090
o-Xylenea 1730 2380 477 1100 11500 9740 2180 830 1760 426
isopropylbenzene 793 1820 116 656 2110 684 942 <300 812 <300 1,2,4-Trimethylbenzeneb 3500 3800 1780 1940 12000 10400 9490 7970 7630 6140
Naphthalene 1820 2080 9450 9120 2740 1170 1890 287 1530 <300
a Value might be high due to coelution with nonane.
b Value might be high due to coelution with decane.
Table A.5—GC Analysis Concentrations Using Average Response Factors (ARF) and Linear Regression (LR) for Vapor Phase Samples (Concentrations in àg/mL)
Compounds
JP-4 Aviation
Fuel No. 2 Fuel Oil (Mean Value)
Mid-Cont Crude (Mean
Value) Alaska Crude Spiked Alaska Crude
ARF LR ARF LR ARF LR ARF LR ARF LR
Butane 60400 58100 <3 <3 37900 44100 45500 53100 122000 14300 n-Hexane 6800 7970 14 14 2450 2930 3900 4630 5460 6573
Benzene 2940 3070 7 5 401 353 962 916 1530 1580
Cyclohexane 1080 1050 28 27 482 441 1450 1470 2740 2980
Toluene 1110 1430 14 14 387 409 404 383 406 378
Octane 175 145 14 12 204 200 210 216 228 236
Ethylbenzene 46.4 <60 6 2 58 58 52 52.1 57.8 57.6
m, p-Xylenes 91.1 44 22 15 158 164 85.6 89.1 87.9 91.4
o-Xylenea <40 <40 5 5 39 42 21.1 21.3 22.4 22.7
isopropylbenzene <40 <40 2 <3 8 4 7.5 4.7 7.83 5.1 1,2,4-Trimethylbenzeneb <40 <40 14 5 13 15 2.1 <3 2.38 <3
Naphthalene <40 <40 2 2 21 13 9.2 <3 1.48 <3
a Value might be high due to coelution with nonane.
b Value might be high due to coelution with decane.
Copyright American Petroleum Institute Provided by IHS under license with API
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Table A.6—Comparision of Predicted Vapor Concentrations Using the Response Factor Analytical Data
Compounds
RKS/Ideal PR/Ideal
Mid-
Cont JP-4 No. 2 FO AK
Crude Spiked
AK Mean Mid-
Cont JP-4 No. 2 FO AK
Crude Spiked
AK Mean Butane 0.99 0.96 NA 0.99 0.99 0.99 0.99 0.97 NA 0.99 0.99 0.99 n-Hexane 1.01 0.96 NA 1.00 1.01 1.01 1.04 1.02 NA 1.04 1.05 1.05 Benzene 1.26 1.38 NA 1.26 1.26 1.26 1.41 1.51 NA 1.41 1.40 1.39 Cyclohexane 1.07 1.13 NA 1.07 1.07 1.07 1.17 1.22 NA 1.17 1.16 1.16 Toluene 1.19 1.30 1.07 1.19 1.19 1.18 1.34 1.44 1.19 1.34 1.33 1.33 Octane 0.97 0.94 1.05 0.96 0.98 0.98 1.05 1.03 1.13 1.05 1.06 1.08 Ethylbenzene 1.05 1.15 0.95 1.05 1.05 1.05 1.21 1.29 1.08 1.21 1.20 1.20
m, p-Xylenes 1.01 1.11 0.91 1.01 1.01 1.01 1.17 1.26 1.04 1.17 1.16 1.16
o-Xylene 1.08 1.20 0.95 1.08 1.08 1.08 1.26 1.37 1.09 1.26 1.25 1.25
Isopropylbenzene 0.86 0.93 0.79 0.86 0.86 0.86 1.00 1.06 0.91 1.00 0.99 0.99 1,2,4 Trimethylbenzene 0.80 0.90 0.71 0.80 0.80 0.80 0.97 1.05 0.84 0.97 0.96 0.96 Naphthalene 1.26 1.54 0.97 1.26 1.25 1.26 1.63 1.89 1.24 1.63 1.60 1.60 Mean 1.04 1.13 0.97 1.04 1.05 1.05 1.19 1.26 1.08 1.19 1.18 1.18 NOTE Ideal = Raoult’s Law; PR = Peng-Robinson equation of state; RKS = Redlich-Kwong-Soave equation of state.
Table A.7—Comparision of Predicted Vapor Concentrations Using the Linear Regression Analytical Data
Compounds
RKS/Ideal PR/Ideal
Mid-
Cont JP-4 No. 2
FO AK Crude
Spiked
AK Mean Mid-
Cont JP-4 No. 2
FO
AK Crude
Spiked
AK Mean Butane 0.98 0.96 NA 0.98 1.04 1.00 0.99 0.97 NA 0.98 1.03 1.00 n-Hexane 1.00 0.98 NA 1.00 1.08 1.03 1.03 1.02 NA 1.03 1.11 1.06 Benzene 1.28 1.38 NA 1.30 1.14 1.25 1.44 1.51 NA 1.45 1.25 1.38 Cyclohexane 1.08 1.13 NA 1.08 1.02 1.06 1.19 1.22 NA 1.19 1.09 1.16 Toluene 1.21 1.29 1.07 1.22 1.08 1.17 1.38 1.43 1.19 1.38 1.20 1.32 Octane 0.96 0.94 1.05 0.96 1.06 0.99 1.05 1.03 1.13 1.04 1.15 1.08 Ethylbenzene 1.07 1.14 0.95 1.07 0.96 1.04 1.24 1.29 1.08 1.24 1.09 1.19
m, p-Xylenes 1.03 1.11 0.91 1.04 0.92 1.00 1.20 1.25 1.04 1.21 1.05 1.15
o-Xylene 1.11 1.20 0.95 1.11 0.97 1.07 1.30 1.37 1.09 1.31 1.11 1.24
Isopropylbenzene 0.87 0.92 0.79 NA 0.80 0.85 1.02 1.06 0.91 NA NA 0.98 1,2,4 Trimethylbenzene 0.82 0.89 0.71 0.83 0.72 0.79 0.99 1.05 0.84 1.00 0.85 0.95 Naphthalene 1.31 1.53 0.97 1.33 1.00 1.23 1.71 1.89 1.24 1.73 NA 1.56 Mean 1.06 1.12 0.97 1.06 0.98 1.04 1.21 1.26 1.08 1.22 1.09 1.17 NOTE Ideal = Raoult’s Law; PR = Peng-Robinson equation of state; RKS = Redlich-Kwong-Soave equation of state.
The compounds chosen for speciation were selected to reflect compounds that: 1) are common to the crude oils and products analyzed; 2) represent a wide volatility range; and 3) are listed as Hazardous Air Pollutants (HAPs) in the Clean Air Act Amendments of 1990. Most of the compounds listed in Table A.3 represent air toxics expected to be present in the crude oils and refined products. Butane, hexane, and octane were selected on the premise that they might contribute significantly to the total vapor above the selected crude oils and refined products.
Liquid and vapor phase concentrations of the 12 chosen compounds were determined by gas chromatography/flame ionization detection (GC/FID). Tables A.4 and A.5 present the liquid and vapor phase concentrations, respectively, using both average response factors (ARF) and linear regression (LR). Liquid and
vapor molecular weights were also measured. --`,,```,,,,````-`-`,,`,,`,`,,`---
The measured liquid concentrations were used as input to a flash calculation routine in the process simulator ASPEN/SP[21] to predict the equilibrium vapor concentrations using Raoult’s Law and the RKS and PR equations of state. The results obtained for the vapor concentrations that were predicted by each equation of state were compared to Raoult’s Law.
Table A.6 and Table A.7 compare the average vapor concentrations that were predicted by the RKS and PR equations of state to those predicted by Raoult’s Law. The tables compare average response factor analytical data and linear regression analytical data. The results are presented in terms of the ratio of the predicted vapor concentration of each equation of state to Raoult’s Law.
The study found that the vapor concentrations predicted by Raoult’s Law and the two equations of state almost agreed. The RKS equation of state predicted vapor concentrations that were about 5 % higher than those predicted by Raoult’s Law, and the PR equation of state predictions were about 18 % higher than Raoult’s Law.
The differences are within the precision and accuracy of the analytical techniques that were used to obtain the compositions in the liquid phase.
It was concluded that there were no advantages in using the equations of state instead of Raoult’s Law, especially since the equations of state are much more difficult to use than Raoult’s Law. It was observed that
“more precise and accurate measurements are possible for liquid samples than for vapor samples, more accurate estimates of air toxics emissions may be possible by predicting vapor compositions based on the measurement of liquid phase concentrations than by measuring vapor concentrations”[14].
The study also concluded that the determination of the liquid molecular weight (ML) is an important factor in predicting the vapor phase equilibrium concentrations. The molecular weight of the liquid is used to convert the liquid phase weight fractions, wi, into mole fractions, xi. These concentrations are then used in Raoult’s Law, RKS, or PR to predict vapor phase mole fractions, yi, as shown in Equation (A.1).
xi = wi (ML /Mi) (A.1)
where
xi = mole fraction of component i in the liquid.
wi = weight fraction of component i in the liquid.
ML = liquid molecular weight, (lb/lb-mole).
Mi = molecular weight of component i in the liquid, (lb/lb-mole).
If the molecular weight of the liquid phase is unknown, it has to be determined. Two analytical methods for determining the molecular weight were used in the study: 1) gel permeation chromatography (GPC) using a refractive index (RI) detector, and 2) gas chromatography (GC) using a flame ionization detector (FID). The GC determination of molecular weight distribution offers better resolution of samples characterized by a low boiling point/MW distribution (boiling point <392 °F or molecular weight <250).
The study did not determine the applicability of Raoult’s Law to mixtures containing hydrocarbon and non–
hydrocarbon constituents, such as reformulated gasolines containing oxygenated species, e.g. MTBE.